Related papers: Coisotropic submanifolds and dual pairs
We give a definition of coisotropic morphisms of shifted Poisson (i.e. $P_n$) algebras which is a derived version of the classical notion of coisotropic submanifolds. Using this we prove that an intersection of coisotropic morphisms of…
In this work, a cosmological model is considered having two scalar fields minimally coupled to gravity with a mixed kinetic term. The model is characterized by the coupling function and the potential function which are assumed to depend on…
We introduce symmetric Poisson structures as pairs consisting of a symmetric bivector field and a torsion-free connection satisfying an integrability condition analogous to that in usual Poisson geometry. Equivalent conditions in Poisson…
We recently obtained the conditions on the couplings of the general two-dimensional massive sigma-model required by (p,q)-supersymmetry. Here we compute the Poisson bracket algebra of the supersymmetry and central Noether charges, and show…
We investigate an extension of 2D nonlinear gauge theory from the Poisson sigma model based on Lie algebroid to a model with additional two-form gauge fields. Dimensional reduction of 3D nonlinear gauge theory yields an example of such a…
In boundary conformal field theories, global symmetries can be broken by boundary conditions, generating a homogeneous conformal manifold. We investigate these geometries, showing they have a coset structure, and give fully worked out…
SYK models provide an interesting playground for exploring the $AdS_2/CFT_1$ correspondence. We focus on a class of SYK models that exhibit higher-spin symmetry, whose gravity sector is described by a BF theory generalizing…
Given a Lie group G whose Lie algebra is endowed with a nondegenerate invariant symmetric bilinear form, we construct a Poisson algebra of continuous functions on a certain open subspace R of the space of representations in G of the…
I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit…
We review the relation between homotopy algebras of conformal field theory and geometric structures arising in sigma models. In particular we formulate conformal invariance conditions, which in the quasi-classical limit are Einstein…
We describe several families of non-unitary coset conformal field theories that possess truly marginal couplings. These generalize the known examples of Wess-Zumino-Witten models on supergroups such as PSU(n|n) or OSP(2n+2|2n). Our…
We formulate interacting antisymmetric tensor gauge theory in a configuration space consisting of a pair of dual field strengths which has a natural symplectic structure. The field equations are formulated as the intersection of a pair of…
We consider the problem of deforming simultaneously a pair of given structures. We show that such deformations are governed by an L-infinity algebra, which we construct explicitly. Our machinery is based on Th. Voronov's derived bracket…
We investigate the differential geometry and topology of globally hyperbolic four-manifolds $(M,g)$ admitting a parallel real spinor $\varepsilon$. Using the theory of parabolic pairs recently introduced in arXiv:1911.08658 , we first…
We survey explicit coordinate descriptions for two (A and X) versions of Teichmuller and lamination spaces for open 2D surfaces, and extend them to the more general set-up of surfaces with distinguished collections of points on the…
We provide a set of theoretical constraints on models in which the Standard Model field content is extended by vector-like fermions and in some cases also by a real scalar singlet. Our approach is based on the study of electroweak vacuum…
Reduction theorem for Poisson manifolds with Hamiltonian Lie algebroids is presented. The notion of compatibility of a momentum section is introduced to the category of Hamiltonian Lie algebroids over Poisson manifolds. It is shown that a…
Chern-Simons gauge theories in 3 dimensions and the Poisson Sigma Model (PSM) in 2 dimensions are examples of the same theory, if their field equations are interpreted as morphisms of Lie algebroids and their symmetries (on-shell) as…
We discuss in details a simple, purely bosonic, quantum field theory belonging to larger class of models with the following properties: a) They are asymptotically free, with a dynamically generated mass scale. b) They have a space of…
For a discrete mechanical system on a Lie group $G$ determined by a (reduced) Lagrangian $\ell$ we define a Poisson structure via the pull-back of the Lie-Poisson structure on the dual of the Lie algebra ${\mathfrak g}^*$ by the…